What is 3/8 plus 3/5? (Answer: 39/40)

Exact Answer

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Problem: What is 3/8 plus 3/5?
Formula / Expression: 3/8 + 3/5
Final Answer: 39/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 5 = 40.
Working: LCD(8, 5) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 3/8 by 5, and multiply the numerator and denominator of 3/5 by 8 so both fractions share the common base 40.
Working: 3 × 5/8 × 5 = 15/40 and 3 × 8/5 × 8 = 24/40

Step 3: Add the Numerators
Now add the numerators (15 + 24 = 39) and keep the common denominator 40 unchanged.
Working: 15 + 24/40 = 39/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 39 and 40 is 1, confirming that 39/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 39/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 40 yields an exact terminating decimal of 0.975 (or 97.5%).
Working: 39 ÷ 40 = 0.975 (97.5%)

Key Values:
- Simplified Fraction: 39/40
- Mixed Number Form: 39/40
- Decimal Value: 0.975
- Percentage: 97.5%

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3/8 + 3/5 = 39/40

Simplified Fraction

39/40

Mixed Number

Proper (39/40)

Decimal Value

0.975

Percentage

97.5%

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Step-by-Step Solution: 3/8 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 5 = 40.

LCD(8, 5) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 3/8 by 5, and multiply the numerator and denominator of 3/5 by 8 so both fractions share the common base 40.

3 × 5/8 × 5 = 15/40 and 3 × 8/5 × 8 = 24/40

Step 3

Add the Numerators

Now add the numerators (15 + 24 = 39) and keep the common denominator 40 unchanged.

15 + 24/40 = 39/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 39 and 40 is 1, confirming that 39/40 cannot be reduced further—it is already in its simplest irreducible form.

39/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 40 yields an exact terminating decimal of 0.975 (or 97.5%).

39 ÷ 40 = 0.975 (97.5%)

Visual Representation

The diagram below illustrates 3/8 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/40`
Mixed Number Form	`39/40`
Decimal Form	`0.975`
Percentage	`97.5%`

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Frequently Asked Questions

What is 3/8 plus 3/5 as a fraction?

3/8 + 3/5 in simplest fraction form is 39/40.

What is 3/8 plus 3/5 as a decimal?

3/8 + 3/5 converted to a decimal is 0.975.

What is 3/8 plus 3/5 as a percentage?

3/8 + 3/5 expressed as a percentage is 97.5%.

Does 3/8 plus 3/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.975) because the denominator in simplest terms contains only prime factors 2 and/or 5.